It takes 1.875 seconds for the ball and the balloon to reach the same height
Step-by-step explanation:
A ball is thrown upward with an initial velocity of 40 feet per second from ground level
- The height of the ball, in feet, after t seconds is given by h= -16 t² + 40 t
At the same time, a balloon is rising at a constant rate of 10 feet per second
- Its height, in feet, after t seconds is given by h = 10 t
We need to find the time it takes for the ball and the balloon to reach the same height
∵ The height of the ball is given by h = -16 t² + 40 t
∵ The height of the balloon is given by h = 10 t
∵ They start at the same time t
∵ They have the same height h
Equate the two equations of h to find t
∴ -16 t² + 40 t = 10 t
- Subtract 10 t from both sides
∴ -16 t² + 30 t = 0
- Take -2 t as a common factor
∴ -2 t(8 t - 15) = 0
Equate -2 t by 0 and 8t - 15 by 0
∵ -2 t = 0 ⇒ divide both sides by -2
∴ t = 0 ⇒ initial time
∵ 8 t - 15 = 0 ⇒ add 15 to both sides
∴ 8 t = 15 ⇒ divide both sides by 8
∴ t = 1.875 seconds
It takes 1.875 seconds for the ball and the balloon to reach the same height
Learn more:
You can learn more about the equations in brainly.com/question/2977815
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